# CAT Quantitative Aptitude Questions | CAT Permutation and Combination Questions

###### CAT Questions | Permutation Probability | GP
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The question is from Permutation and Combination. A question which combines probability with progression. Our task is to identify the infinite series which is ultimately the probability of that given event. This section hosts a number of questions which are on par with CAT questions in difficulty on CAT Permutation and Combination, and CAT Probability.

Question 14: A and B take part in a duel. A can strike with an accuracy of 0.6. B can strike with an accuracy of 0.8. A has the first shot, post which they strike alternately. What is the probability that A wins the duel?

1. $$frac{7}{10}\\$ 2. $\frac{15}{23}\\$ 3. $\frac{2}{3}\\$ 4. $\frac{11}{17}\\$ ## Try 2IIM Online CAT Coaching #### Best CAT Online Coaching ### Video Explanation ## Best CAT Coaching in Chennai #### Batches filling fast. Starts Sat, April 27th, 2019 ### Explanatory Answer ##### Method of solving this CAT Question from Permutation and Combination: One unit number theory and one unit Combinatorics makes a potent combination for fabulous questions! A can win in the following scenarios: A strikes in first shot. A misses in the first shot, B misses in the second, A strikes in the third. A misses in the 1st shot, B misses in the 2nd, A misses the 3rd, B misses the 4th and A strikes the 5th. And so on… P$A in 1st shot) = 0.6
P(A in 3rd shot) = 0.4 * 0.2 * 0.6 {A misses, then B misses and then A strikes}
P(A in 5st shot) = 0.4 * 0.2 * 0.4 * 0.2 * 0.6 {A misses, then B misses and then A misses, then B misses, then A strikes}
Overall probability = Sum of all these

= 0.6 + 0.4 * 0.2 * 0.6 + 0.4 * 0.2 * 0.4 * 0.2 * 0.6 + …
Which is nothing but
0.6 + (0.4 * 0.2) * 0.6 + (0.4 * 0.2)2 * 0.6 + (0.4 * 0.2)3 * 0.6…

This is an infinite geometric progression with first term 0.6 and common ratio 0.4 * 0.2
Required Probability = $$frac{a}{1 - r}\\$ = $\frac{0.6}{1 - 0.08}\\$ = $\frac{0.6}{0.92}\\$ = $\frac{30}{46}\\$ = $\frac{15}{23}\\$ The question is "What is the probability that A wins the duel?" ##### Hence the answer is "$\frac{15}{23}\\$" Choice B is the correct answer. ###### Best Online CAT CoachingLearn from 4 time CAT 100 percentiler Register in 2 easy steps and start learning in 30 seconds! ###### Already have an Account? ###### CAT Coaching in Chennai Next Weekend Batch Starts Sat, April 27th, 2019 ###### Best CAT Coaching in ChennaiBatches filling fast Personalised attention, Small batch sizes. ## CAT Preparation Online | CAT Permutation and Combination; Probability Videos On YouTube #### Other useful sources for Permutation and Combination Questions | Probability Questions ##### Where is 2IIM located? 2IIM Online CAT Coaching A Fermat Education Initiative, 10-C, Kalinga Colony, Bobbili Raja Salai K.K.Nagar, Chennai. India. Pin - 600 078 ##### How to reach 2IIM? Phone:$91) 44 4505 8484
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